Active photonic devices incorporating high dielectric constant materials

ABSTRACT

An optical switch structure includes a substrate, a first electrical contact, and a first material having a first conductivity type electrically connected to the first electrical contact. The optical switch structure also includes a second material having a second conductivity type coupled to the first material, a second electrical contact electrically connected to the second material, and a waveguide structure disposed between the first electrical contact and the second electrical contact. The waveguide structure includes a waveguide core coupled to the substrate and including a first material characterized by a first index of refraction and a first electro-optic coefficient and a waveguide cladding at least partially surrounding the waveguide core and including a second material characterized by a second index of refraction less than the first index of refraction and a second electro-optic coefficient greater than the first electro-optic coefficient.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/365,543, filed on Mar. 26, 2019; which claims priority to U.S.Provisional Patent Application No. 62/819,765, filed on Mar. 18, 2019,the disclosures of which are hereby incorporated by reference in theirentirety for all purposes.

BACKGROUND OF THE INVENTION

Electro-optic (EO) modulators and switches have been used in opticalfields. Some EO modulators utilize free-carrier electro-refraction,free-carrier electro-absorption, or the DC Kerr effect to modify opticalproperties during operation, for example, to change the phase of lightpropagating through the EO modulator or switch. As an example, opticalphase modulators can be used in integrated optics systems, waveguidestructures, and integrated optoelectronics.

Despite the progress made in the field of EO modulators and switches,there is a need in the art for improved methods and systems related toEO modulators and switches.

SUMMARY OF THE INVENTION

Embodiments of the present invention generally relate to photonicdevices. More particularly, embodiments of the present invention relateto active photonic devices utilized as components of optical modulatorsand optical switches. In a particular embodiment, active photonicdevices including waveguide cladding materials characterized by highelectro-optic coefficients are utilized to improve modulation and/orswitching performance. Moreover, in another embodiment, active photonicdevices including waveguide cladding materials characterized by highdielectric constants are utilized to improve modulation and/or switchingperformance. The present invention has applicability to a wide varietyof photonic and opto-electronic devices.

According to an embodiment of the present invention, a waveguidestructure is provided. The waveguide structure includes a substrate, awaveguide core coupled to the substrate and including a first materialcharacterized by a first index of refraction and a first dielectricconstant, and a waveguide cladding at least partially surrounding thewaveguide core and including a second material characterized by a secondindex of refraction less than the first index of refraction and a seconddielectric constant greater than the first dielectric constant.

In some embodiments, the first material comprises silicon, the firstdielectric constant is 11.7, and the second dielectric constant isgreater than 11.7. As examples, the second material can include HfO₂,Ta₂O₅, or ZrO₂. In an alternative embodiment, the waveguide structurefurther includes a set of electrodes operable to establish an electricfield across the waveguide cladding and the waveguide core. A voltagedrop across the waveguide core is greater than a voltage drop across thewaveguide cladding. Furthermore, in some embodiments, the waveguidestructure also includes a second cladding layer coupled to the waveguidecladding. The first material is characterized by a first electro-opticcoefficient, the second material is characterized by a secondelectro-optic coefficient greater than the first electro-opticcoefficient, and the second cladding layer includes a third materialcharacterized by a third electro-optic coefficient greater than thefirst electro-optic coefficient.

According to another embodiment of the present invention, an opticalswitch structure is provided. The optical switch structure includes asubstrate, a first electrical contact, and a first material having afirst conductivity type electrically connected to the first electricalcontact. The optical switch structure also includes a second materialhaving a second conductivity type coupled to the first material and asecond electrical contact electrically connected to the second material.The optical switch structure further includes a waveguide structuredisposed between the first electrical contact and the second electricalcontact. The waveguide structure includes a waveguide core coupled tothe substrate and including a first material characterized by a firstindex of refraction and a first electro-optic coefficient (e.g., havinga value of approximately zero) and a waveguide cladding at leastpartially surrounding the waveguide core and including a second materialcharacterized by a second index of refraction less than the first indexof refraction and a second electro-optic coefficient greater than thefirst electro-optic coefficient.

In an embodiment, the waveguide core supports a guided modecharacterized by an optical power. A majority of the optical power iscontained in the waveguide core. The waveguide core can include siliconor can consist of silicon. In some embodiments, the waveguide core cansupport a TE polarization mode.

According to a specific embodiment of the present invention, a waveguidestructure is provided. The waveguide structure includes a substrate anda waveguide core coupled to the substrate and including a first materialcharacterized by a first index of refraction and a first electro-opticcoefficient. The waveguide structure also includes a first claddinglayer at least partially surrounding the waveguide core and including asecond material characterized by a second index of refraction less thanthe first index of refraction and a second electro-optic coefficientgreater than the first electro-optic coefficient and a second claddinglayer coupled to the first cladding layer. The waveguide core caninclude silicon, the first cladding layer comprises tantalum oxide, andthe second cladding layer comprises silicon dioxide.

The second cladding layer can include a third material characterized bya third electro-optic coefficient greater than the first electro-opticcoefficient. The second electro-optic coefficient and the thirdelectro-optic coefficient can be greater than or equal to anelectro-optic coefficient for silicon. In some embodiments, the thirdelectro-optic coefficient is less than the second electro-opticcoefficient. As an example, the waveguide cladding can include 200 nm ofthe second material proximal to the waveguide core and 2 μm of the thirdmaterial distal to the waveguide core. The second material, for example,tantalum oxide (Ta₂O₅), can be characterized by a χ⁽³⁾ value greaterthan 2.2×10⁻¹⁸ m²/W. In other embodiments, the second material, forexample, lead zirconate titanate (PZT) or barium titanate (BaTiO₃), canbe characterized by a χ⁽²⁾ value greater than zero, greater than 10pm/V, or greater than 100 pm/V. The waveguide structure can include aMach-Zehnder interferometer or a ring resonator.

According to another specific embodiment of the present invention, anoptical switch structure is provided. The optical switch structureincludes a substrate, a waveguide structure coupled to the substrate,and a set of electrodes positioned adjacent the waveguide structure. Theset of electrodes are configured to establish an applied electric fieldhaving a component oriented along a lateral direction. The waveguidestructure includes a waveguide core configured to support a guided modepolarized along the lateral direction and propagating along alongitudinal direction orthogonal to the lateral direction and includinga first material characterized by a first index of refraction and afirst electro-optic coefficient. The waveguide core can include siliconor consist of silicon. The guided mode can include a TE polarizationmode. The waveguide structure also includes a waveguide cladding atleast partially surrounding the waveguide core and including a secondmaterial characterized by a second index of refraction less than thefirst index of refraction and a second electro-optic coefficient tensorhaving a maximum value aligned with the lateral direction.

In an embodiment, the first electro-optic coefficient and the secondelectro-optic coefficient are the Kerr coefficient χ⁽³⁾. In anotherembodiment, the first electro-optic coefficient and the secondelectro-optic coefficient are the Pockels coefficient χ⁽²⁾.

According to a particular embodiment of the present invention, anoptical switch structure is provided. The optical switch structureincludes at least one optical input port and at least one optical outputport. The at least one optical output port can include a first opticaloutput port and a second optical output port. The optical switchstructure also includes an optical waveguide structure including awaveguide core (e.g., silicon) and a waveguide cladding. The opticalwaveguide structure is optically coupled to the at least one opticalinput port. The waveguide core includes a first material characterizedby a first index of refraction and a first electro-optic coefficient andthe waveguide cladding includes a second material characterized by asecond index of refraction less than the first index of refraction and asecond electro-optic coefficient greater than the first electro-opticcoefficient.

In an embodiment, the first electro-optic coefficient and the secondelectro-optic coefficient are the Kerr coefficient χ⁽³⁾. In anotherembodiment, the first electro-optic coefficient and the secondelectro-optic coefficient are the Pockels coefficient χ⁽²⁾. Thewaveguide core can support a guided mode characterized by an opticalpower, with the majority of the optical power being contained in thewaveguide core.

In a particular embodiment, the optical switch structure furtherincludes a first electric contact and a second electrical contactconfigured to generate an applied electric field produced in the opticalwaveguide structure that is characterized by a direction and thewaveguide cladding is characterized by an electro-optic coefficienttensor having a maximum value aligned along the direction. The guidedmode supported by the waveguide core can have a direction ofpolarization aligned with the direction. As an example, the waveguidecladding can be characterized by a DC Kerr effect and a Pockels effecthaving a same sign. For instance, the DC Kerr effect can be positive andthe Pockels effect can be positive. The waveguide cladding can include afirst material type, with a majority of polarization domains beingaligned with a positive z-direction, and a direction of the appliedelectric field can be negative.

In another embodiment, the waveguide cladding includes a first materialtype, a majority of polarization domains are aligned with a negativez-direction, and a direction of the applied electric field is positive.In yet another embodiment, the waveguide cladding includes a secondmaterial type, a majority of polarization domains are aligned with apositive z-direction, and a direction of the applied electric field ispositive. In a particular embodiment, the waveguide cladding includes asecond material type, a majority of polarization domains are alignedwith a negative z-direction, and a direction of the applied electricfield is negative.

According to another particular embodiment of the present invention, anintegrated optical system is provided. The integrated optical systemincludes a cryostat and a device disposed in the cryostat. The deviceincludes an electro-optic switch including at least one input port, afirst beam splitter, and a Mach-Zehnder interferometer coupled to thefirst beam splitter. The Mach-Zehnder interferometer includes a phaseadjustment region including a waveguide core characterized by a firstdielectric constant and a waveguide cladding at least partiallysurrounding the waveguide core and including a second materialcharacterized by a second dielectric constant greater than the firstdielectric constant. The device also includes a second beam splittercoupled to the Mach-Zehnder interferometer and a set of output portscoupled to the second beam splitter.

The waveguide core can include silicon, the first dielectric constantcan be 11.7, and the second dielectric constant can be greater than11.7. As an example, the second material can include HfO₂, Ta₂O₅, orZrO₂. In an embodiment, the integrated optical system further includes aset of electrodes operable to establish an electric field across thewaveguide cladding and the waveguide core. A voltage drop across thewaveguide core is greater than a voltage drop across the waveguidecladding. In another embodiment, the integrated optical system furtherincludes a second cladding layer coupled to the waveguide cladding. Inthis embodiment, the waveguide core is characterized by a firstelectro-optic coefficient, the second material is characterized by asecond electro-optic coefficient greater than the first electro-opticcoefficient, and the second cladding layer includes a third materialcharacterized by a third electro-optic coefficient greater than thefirst electro-optic coefficient.

According to another embodiment of the present invention, an opticalswitch structure is provided. The optical switch structure includes asubstrate, a waveguide structure coupled to the substrate, and a set ofelectrodes positioned adjacent the waveguide structure. The set ofelectrodes are configured to establish an applied electric field havinga component oriented along a lateral direction. The waveguide structureincludes a waveguide core configured to support a guided modepropagating along a longitudinal direction orthogonal to the lateraldirection and including a first material characterized by a first indexof refraction and a first electro-optic coefficient and a waveguidecladding at least partially surrounding the waveguide core and includinga second material characterized by a second index of refraction lessthan the first index of refraction and a second electro-opticcoefficient. The waveguide cladding is characterized by a DC Kerrcoefficient χ⁽³⁾ and a Pockels coefficient χ⁽²⁾ that are both associatedwith a positive change in index of refraction.

Numerous benefits are achieved by way of the present disclosure overconventional techniques. For example, embodiments of the presentinvention provide methods and systems that can utilize a reduced appliedbias to achieve a given electric field in a waveguide core, therebyreducing power consumption and increasing efficiency. Moreover,embodiments of the present invention enable larger changes in effectiveindex of refraction than using conventional techniques. As a result,device length can be decreased, which, in turn, reduces optical lossesand saves space. These and other embodiments of the disclosure alongwith many of its advantages and features are described in more detail inconjunction with the text below and attached figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified schematic diagram illustrating an optical switchaccording to an embodiment of the present invention.

FIG. 2 is a simplified schematic diagram showing a top view of an activewaveguide region according to an embodiment of the present invention.

FIG. 3 is a simplified schematic diagram illustrating a p-n diodewaveguide structure incorporating high-κ materials according to anembodiment of the present invention.

FIG. 4 is a simplified schematic diagram illustrating a p-i-n diodewaveguide structure incorporating high-κ materials according to anembodiment of the present invention.

FIG. 5 is a simplified schematic diagram illustrating a vertical pinwaveguide structure incorporating high-κ materials according to anembodiment of the present invention

FIG. 6 is a simplified schematic diagram illustrating adielectric-waveguide-dielectric structure incorporating high-κ materialsaccording to an embodiment of the present invention.

FIG. 7A is a simplified schematic diagram illustrating a p-n diodewaveguide structure incorporating electro-optic cladding materialsaccording to an embodiment of the present invention.

FIG. 7B is a simplified schematic diagram illustrating a p-n diodewaveguide structure incorporating a planar electro-optic cladding layeraccording to an embodiment of the present invention.

FIG. 7C is a simplified schematic diagram illustrating a buriedwaveguide structure incorporating a planar electro-optic cladding layeraccording to an embodiment of the present invention.

FIG. 7D is a simplified schematic diagram illustrating a buriedwaveguide structure incorporating a planar electro-optic cladding layeraccording to another embodiment of the present invention.

FIG. 7E is a simplified schematic diagram illustrating a waveguidestructure incorporating electro-optic cladding materials according to anembodiment of the present invention.

FIG. 8 is a simplified schematic diagram illustrating a p-i-n diodewaveguide structure incorporating electro-optic cladding materialsaccording to an embodiment of the present invention.

FIG. 9 is a simplified schematic diagram illustrating a vertical pinwaveguide structure incorporating high-κ materials according to anembodiment of the present invention.

FIG. 10 is a simplified schematic diagram illustrating adielectric-waveguide-dielectric structure incorporating electro-opticcladding materials according to an embodiment of the present invention.

FIG. 11 is a simplified system diagram illustrating incorporation of anelectro-optic switch with a dewar according to an embodiment of thepresent invention.

FIG. 12A is a graph plotting the DC Kerr effect as a function of appliedelectric field for a first material type according to an embodiment ofthe present invention.

FIG. 12B is a graph plotting the Pockels effect as a function of appliedelectric field for a first material type according to an embodiment ofthe present invention.

FIG. 12C is a graph plotting the DC Kerr effect as a function of appliedelectric field for a second material type according to an embodiment ofthe present invention.

FIG. 12D is a graph plotting the Pockels effect as a function of appliedelectric field for a second material type according to an embodiment ofthe present invention.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the present invention relate to optical systems. Moreparticularly, embodiments of the present invention utilize highdielectric constant materials (i.e., high-κ materials) in opticalmodulators and switches to reduce power consumption during operation.Merely by way of example, embodiments of the present invention areprovided in the context of integrated optical systems that includeactive optical devices, but the invention is not limited to this exampleand has wide applicability to a variety of optical and optoelectronicsystems.

According to some embodiments, the active photonic devices describedherein utilize electro-optic effects, such as free carrier inducedrefractive index variation in semiconductors, the Pockels effect, and/orthe DC Kerr effect to implement modulation and/or switching of opticalsignals. Thus, embodiments of the present invention are applicable toboth modulators, in which the transmitted light is modulated either ONor OFF, or light is modulated with a partial change in transmissionpercentage, as well as optical switches, in which the transmitted lightis output on a first output (e.g., waveguide) or a second output (e.g.,waveguide) or an optical switch with more than two outputs, as well asmore than one input. Thus, embodiments of the present invention areapplicable to a variety of designs including an M(input)×N(output)systems that utilize the methods, devices, and techniques discussedherein.

FIG. 1 is a simplified schematic diagram illustrating an optical switchaccording to an embodiment of the present invention. Referring to FIG.1, switch 100 includes two inputs: Input 1 and Input 2 as well as twooutputs: Output 1 and Output 2. As an example, the inputs and outputs ofswitch 100 can be implemented as optical waveguides operable to supportsingle mode or multimode optical beams. As an example, switch 100 can beimplemented as a Mach-Zehnder interferometer integrated with a set of50/50 beam splitters 105 and 107, respectively. As illustrated in FIG.1, Input 1 and Input 2 are optically coupled to a first 50/50 beamsplitter 105, also referred to as a directional coupler, which receiveslight from the Input 1 or Input 2 and, through evanescent coupling inthe 50/50 beam splitter, directs 50% of the input light from Input 1into waveguide 110 and 50% of the input light from Input 1 intowaveguide 112. Concurrently, first 50/50 beam splitter 105 directs 50%of the input light from Input 2 into waveguide 110 and 50% of the inputlight from Input 2 into waveguide 112. Considering only input light fromInput 1, the input light is split evenly between waveguides 110 and 112.

Mach-Zehnder interferometer 120 includes phase adjustment section 122.Voltage V₀ can be applied across the waveguide in phase adjustmentsection 122 such that it can have an index of refraction in phaseadjustment section 122 that is controllably varied. Because light inwaveguides 110 and 112 is in-phase after propagation through the first50/50 beam splitter 105, phase adjustment in phase adjustment section122 can introduce a predetermined phase difference between the lightpropagating in waveguides 130 and 132. As will be evident to one ofskill in the art, the phase relationship between the light propagatingin waveguides 130 and 132 can result in output light being present atOutput 1 (e.g., light beams are in-phase) or Output 2 (e.g., light beamsare out of phase), thereby providing switch functionality as light isdirected to Output 1 or Output 2 as a function of the voltage V₀ appliedat the phase adjustments section 122. Although a single active arm isillustrated in FIG. 1, it will be appreciated that both arms of theMach-Zehnder interferometer can include phase adjustment sections.

As illustrated in FIG. 1, electro-optic switch technologies, incomparison to all-optical switch technologies, utilize the applicationof the electrical bias (e.g., V₀ in FIG. 1) across the active region ofthe switch to produce optical variation. The electric field and/orcurrent that results from application of this voltage bias results inchanges in one or more optical properties of the active region, such asthe index of refraction or absorbance. In addition to the powerdissipated by current flow (in the cases where a current results fromthe application of the bias voltage), energy is dissipated by thecreation of the electric field, which has an energy density of E²κ/8π(cgs units), where E is the electric field and κ is the dielectricconstant.

Although a Mach-Zehnder interferometer implementation is illustrated inFIG. 1, embodiments of the present invention are not limited to thisparticular switch architecture and other phase adjustment devices areincluded within the scope of the present invention, including ringresonator designs, Mach-Zehnder modulators, generalized Mach-Zehndermodulators, and the like. One of ordinary skill in the art wouldrecognize many variations, modifications, and alternatives.

The inventors have determined that because the energy density is higherin regions with a high dielectric constant, incorporation of high-κmaterials into the electro-optic switch architecture can reduce theoverall power consumption of the electro-optic switch because the energydensity is proportional to the square of the electric field which, in amultilayer device, is inversely proportional to the dielectric constant.The impact of the dielectric constant of the optical materials isillustrated with respect to FIG. 2.

FIG. 2 is a simplified schematic diagram showing a top view of an activewaveguide region according to an embodiment of the present invention. InFIG. 2, metal electrodes 210 and 212 are positioned on either side ofwaveguide core 220, which is disposed between waveguide cladding regions222 and 224. In this implementation, the waveguide core 220 isfabricated using silicon and the waveguide cladding regions 222 and 224are fabricated using silicon dioxide. The dielectric constants of thematerials are represented by the κ values of 11.7 for Si and 3.9 forSiO₂. The thickness of the layers (i.e., d_(Si) and d_(ox)) as well asthe electric field in each layer (i.e., E_(Si) and E_(ox)) are alsoillustrated.

When an electric field is applied across the waveguide structure by theapplication of a voltage bias to the metal electrodes 210 and 212, theindex of refraction in the waveguide core 220 and the waveguide claddingregions 222 and 224 is altered, through the DC Kerr effect. As describedin relation to FIG. 1, incorporation of an active region (i.e., a phaseadjustment section) as illustrated in FIG. 2 can be utilized toimplement an electro-optic switch.

Because the displacement field perpendicular to the layers (D=κE) mustbe continuous, E_(Si)=(3.9/11.7)E_(ox)=E_(ox)/3.

Thus, a significant portion of the electric field bias applied acrossthe phase adjustment section device is dropped across the silicondioxide cladding regions 222 and 224, which have low-κ values incomparison to the silicon waveguide core, thereby failing to produce thedesired index of refraction change in the silicon waveguide core as thebias is dropped across the low-κ silicon dioxide layers. Given typicalvalues for the waveguide layers designed to operate at 1.55 μm ofd_(Si)=0.5 μm and d_(ox)=0.5 μm, which is approximately the minimumdistance suitable for avoiding optical absorption by the metalelectrodes, the potential drop across the silicon layer for an appliedvoltage bias of V₀ is only V₀/7. Thus, 6/7 of the applied voltage biasis dropped across the silicon oxide layers.

The capacitance of the device schematically illustrated in FIG. 2 perunit area is C/A=1.67/4πd, in the case where d=d_(ox)=d_(Si) and thelayer capacitances are added in series using cgs units. If the SiO₂ isreplaced with a high-κ dielectric the power consumption during operationis reduced significantly. In an embodiment, hafnium dioxide (HfO₂) isutilized in place of the silicon dioxide cladding layers. Assuming atypical dielectric constant for HfO₂ of 39, the potential drop acrossthe silicon waveguide core becomes 5V/8 because, E_(Si)=(39/11.7)E_(ox)=10E_(ox)/3.

The capacitance/area becomes C/A=7.35/4πd. Thus, replacing the silicondioxide cladding layers with hafnium dioxide cladding layers enablesembodiments of the present invention to lower the applied bias V₀ by afactor of (5/8)/(1/7)=35/8 while maintaining the same electric field inthe silicon waveguide core, thereby achieving the same switching effect.Power reductions of this sort are of particular benefit to cryogenicelectro-optic switches due to the difficulty in creating high voltagedrivers that operate at low temperatures.

Because the energy per unit area required to charge the capacitance isequal to 0.5CV²/A, replacing the silicon dioxide cladding layers withhafnium dioxide cladding layers reduces the required switching energy bya factor of (1.67/7.35)*(35/8)²=4.4. Thus, embodiments of the presentinvention enable substantial energy savings over conventional designs.One of skill in the art will appreciate that the model discussed inrelation to FIG. 2 is utilized merely to demonstrate the impact ofutilizing high-κ dielectric materials in active devices since actualdevice geometries will not typically achieve benefits associated withthe schematic system illustrated in FIG. 2. There will, however, stillbe significant advantages for typical device designs, including bothcarrier and Kerr based switches, because the high-κ dielectric can beused to force higher electric fields in the lower κ active area of thedevice while reducing or minimizing the overall required energy.

Although the discussion in relation to FIG. 2 has been provided inrelation to the voltage and electric field being applied in the plane ofthe figure, this is not required by the present invention and otherembodiments that are implemented in a “vertical” design are includedwithin the scope of the present invention. Accordingly, the variousmaterials can be formed using epitaxial growth, deposition, layertransfer, or the like to fabricate a structure in which the electricfield is directed from upper layers of the structure to bottom layers orvice versa. One of ordinary skill in the art would recognize manyvariations, modifications, and alternatives.

FIG. 3 is a simplified schematic diagram illustrating a p-n diodewaveguide structure incorporating high-κ materials according to anembodiment of the present invention. Referring to FIG. 3, thecross-section of the p-n diode waveguide structure includes anillustration of substrate 310, which supports waveguide layer 320, whichincludes p+ contact region 322, p-type region 324, n-type region 326,and n+ contact region 328. In some embodiments, the substrate 310 is theburied oxide (BOX) layer of a silicon-on-insulator (SOI) structure,although this is not required by the present invention. Metal contacts330 and 332 are provided to enable application of a voltage bias acrossthe silicon waveguide core 340. Although in the embodiment illustratedin FIG. 3, a silicon waveguide core 340 is utilized, embodiments of thepresent invention are not limited to silicon for the waveguide corematerial and other materials including silicon nitride-based materials,silicon-germanium-based materials, or combinations thereof are includedwithin the scope of the present invention.

Cladding material 350 disposed on either side of the silicon waveguidecore 340 is fabricated using a high-κ material, for example, hafniumoxide (HfO₂). In some embodiments, a single transverse mode siliconwaveguide structure is utilized with the width of the waveguide core 340being in the sub-micron to micron range. In other embodiments, multimodewaveguide structures are utilized with a wider waveguide core thatsupports two or more transverse modes. One of ordinary skill in the artwould recognize many variations, modifications, and alternatives.

Characteristics of the cladding include the index of refraction (n),optical loss (the imaginary part of the index of refraction), and thedielectric constant (κ). The index of refraction can be considered asthe square root of the high frequency (i.e., optical frequencies)dielectric constant whereas the dielectric constant κ can be consideredas the low frequency (i.e. up to, for example, GHz frequencies)dielectric constant. Hafnium oxide is suitable for use in embodiments ofthe present invention since it is characterized by a high κ, has a widebandgap, has an index of refraction of approximately n=2.0 (e.g., in thevisible and near infrared), thereby providing a lower index ofrefraction than the silicon waveguide core, and exhibits low absorptionat infrared wavelengths. Because the optical mode is present not only inthe waveguide, but in the cladding as determined by the mode profile,low absorption by the cladding at the operating wavelength is utilizedin some embodiments to provide low optical loss for the optical modepropagating in the waveguide.

In order to vary the index of refraction in the waveguide core, avoltage bias is applied using metal contacts 330 and 332, also referredto as electrodes. As an example, the p-n junction can be placed underreverse bias, generating a depletion region at the p-n junctioninterface. Thus, application of the reverse voltage bias will result ingeneration of an electric field in the waveguide core as well as in thecladding regions as discussed in relation to FIG. 2. As discussed above,the incorporation of the high-κ cladding material will result in anincreased percentage of the applied bias being dropped across thewaveguide core, thereby either increasing the index of refraction changeat a given voltage bias or providing a given index of refraction changeat a lower voltage bias.

Although a reverse biased junction is utilized in some embodiments,forward biasing of the p-n junction and the resulting current injectionthat will be produced can also be utilized to achieve variation of thecomplex index of refraction in the waveguide. As will be evident to oneof skill in the art, increasing the free carrier concentration willdecrease the real part of the index of refraction and increase theimaginary part (i.e., the imaginary part being proportional to theabsorption). Introducing an electric field will increase the index ofrefraction through the DC Kerr effect. Thus, forward bias operation isutilized in some embodiments. Operation using forward bias can be usedto change the index via a current, which can result in a level of powerconsumption. It will be appreciated that in the case of forward biasoperation, rather than increasing or maximizing the electric field inthe active region, a current is injected that that flows at a low bias,thereby utilizing a structure with a reduced or minimized resistance.Moreover, it will be appreciated that devices provided according toembodiments of the present invention may not simultaneously utilize theDC Kerr effect (e.g., through application of an electric field) andfree-carrier electrorefraction (e.g., by introducing carriers) becausethese effects generally oppose each other. One of ordinary skill in theart would recognize many variations, modifications, and alternatives.

The use of the high-κ material for the cladding will, for a given changeindex of refraction, enable the use of lower bias voltages and consumeless energy than conventional designs in which the cladding regionssurrounding the waveguide core do not have a higher dielectric constant.As a result, when utilized in a switch or modulator, the desired phaseadjustment, for example, to introduce a π phase shift between the armsof an interferometer, can be achieved at lower applied voltage and, as aresult, can consume less energy. Thus, embodiments of the presentinvention enable the incorporation of high-κ material to reduce theenergy consumption associated with electro-optic switches. As describedherein, embodiments of the present invention enable cryogenic operation

By incorporating high-κ cladding materials, operation of switches atenergies below 10 pJ is enabled; for example, operation at energies inthe range of 100 fJ to 10 pJ are possible. In comparison, conventionaldielectric materials, such as silicon dioxide, may not be able toachieve operation at these low energies as a result of the smallfraction of the voltage bias that is dropped across the waveguide core.Thus, embodiments of the present invention enable operation of devicesthat enjoy the benefits of resonant structures, but with reducedmanufacturing tolerances. As an example, embodiments of the presentinvention can provide performance comparable to that achieved using someform of resonant enhancement (for example, a ring or photonic crystal).However, these performance benefits are achieved with a reduction indrawbacks associated with resonant enhancement, for example, the needfor very tight manufacturing tolerances to achieveuniformity/reproducibility in performance.

In integrated electro-optics implementations in which multiple switchesare operated as components of a larger system, local temperatureincreases as a result of energy deposition in the switch components canresult in the operation of the switch, as well as neighboring switchesand components that fall outside system specifications. Thus, bothtemporal as well as spatial variations in temperature across anintegrated optics device can be prevented using embodiments of thepresent invention. As an example, in the Mach-Zehnder interferometerillustrated in FIG. 1, increase in temperature of the phase adjustmentsection can result in an increase in the index of refraction, resultingin unbalancing of the arms of the interferometers. Thus, the low energyoperation provided by embodiments of the present invention enables thedevelopment and production of integrated optics systems that are notachievable using conventional techniques. This is particularly true foroperation at low temperatures, for example, at liquid heliumtemperatures.

Although a silicon waveguide core and hafnium oxide cladding is utilizedin the embodiment illustrated in FIG. 3, other materials can be utilizedaccording to embodiments of the present invention. For example, inaddition to silicon, other materials including SiN, Ge, SiGe, andvarious polymers can be utilized for the waveguide core. Moreover, inaddition to hafnium dioxide, other materials including tantalum oxide(Ta₂O₅), zirconium oxide (ZrO₂), titanium dioxide (TiO₂), otherrefractory metal oxides, combinations thereof, or the like can beutilized for the waveguide cladding.

FIG. 4 is a simplified schematic diagram illustrating a p-i-n diodewaveguide structure incorporating high-κ materials according to anembodiment of the present invention. The p-i-n diode waveguide structureillustrated in FIG. 4 shares similarities with the p-n diode waveguidestructure illustrated in FIG. 3 and the discussion provided in relationto FIG. 3 is applicable to FIG. 4 as appropriate.

Referring to FIG. 4, the cross-section of the p-i-n diode waveguidestructure includes an illustration of substrate 410, which supportswaveguide layer 420, which includes p+ contact region 422, p-type region424, intrinsic region 425, n-type region 426, and n+ contact region 428.In some embodiments, the substrate 410 is the buried oxide (BOX) layerof a silicon-on-insulator (SOI) structure, although this is not requiredby the present invention. Metal contacts 430 and 432 are provided toenable application of a voltage bias across the silicon waveguide core440. Cladding material 450 disposed on either side of the siliconwaveguide core 440 is fabricated using a high-κ material, for example,hafnium oxide (HfO₂). Hafnium oxide is suitable for use in embodimentsof the present invention since it is characterized by a high κ, has awide bandgap, has an index of refraction of approximately n=2.0, therebyproviding a lower index of refraction than the silicon waveguide core440, and exhibits low absorption at infrared wavelengths. Because theoptical mode is present not only in the waveguide, but in the claddingas determined by the mode profile, low absorption by the cladding at theoperating wavelength is utilized in some embodiments to provide lowoptical loss for the optical mode propagating in the waveguide.

In order to vary the index of refraction in the waveguide core, avoltage bias is applied using metal contacts 430 and 432, also referredto as electrodes. As an example, the p-i-n junction can be placed underreverse bias, generating a depletion region in the intrinsic region 425.Thus, application of the reverse voltage bias will result in generationof an electric field in the waveguide core as well as in the claddingregions as discussed in relation to FIG. 2. As discussed above, theincorporation of the high-κ cladding material will result in anincreased percentage of the voltage bias being dropped across thewaveguide core, thereby either increasing the index of refraction changeat a given voltage bias or providing a given index of refraction changeat a lower voltage bias.

Although a silicon waveguide core and hafnium oxide cladding areutilized in the embodiment illustrated in FIG. 4, other materials can beutilized according to embodiments of the present invention. For example,in addition to silicon, other materials including SiN, Ge, SiGe, andvarious polymers can be utilized for the waveguide core. Moreover, inaddition to hafnium dioxide, other materials including tantalum oxide(Ta₂O₅), zirconium oxide (ZrO₂), titanium dioxide (TiO₂), otherrefractory metal oxides, combinations thereof, or the like can beutilized for the waveguide cladding.

FIG. 5 is a simplified schematic diagram illustrating a vertical pinwaveguide structure incorporating high-κ materials according to anembodiment of the present invention. The vertical pin waveguidestructure illustrated in FIG. 5 shares similarities with the p-n diodewaveguide structure illustrated in FIG. 3 and the discussion provided inrelation to FIG. 3 is applicable to FIG. 5 as appropriate.

Referring to FIG. 5, the cross-section of the vertical pin waveguidestructure includes an illustration of substrate 510, which supportswaveguide region 520, which includes p+ contact region 522, p-typeregion 524, n-type region 526, and n+ contact region 528. The opticalwaveguide is defined by the p-type region 524, intrinsic silicon layer515, and the n-type region 526. In some embodiments, the substrate 510is the buried oxide (BOX) layer of a silicon-on-insulator (SOI)structure, although this is not required by the present invention. Metalcontacts 530 and 532 are provided to enable application of a voltagebias across the vertical pin formed by the p-type region 524, theintrinsic layer 515, and the n-type region 526. Cladding material 550 isdisposed on either side of the vertical pin and is fabricated using ahigh-κ material, for example, hafnium oxide (HfO₂).

In the vertical pin waveguide structure illustrated in FIG. 5, a guidedmode is supported with a peak amplitude that is generally aligned withthe intrinsic layer 515. The intrinsic layer 515 can be fabricated usinga suitable undoped or low-doped semiconductor, for example, silicon ifp-type region 524 and n-type region 526 are silicon. In someembodiments, the thickness of the intrinsic layer 515 ranges from about0 nm to about 100 nm, for example, 30 nm.

In some embodiments, biasing of the metal contacts 530 and 532 canresult in carrier accumulation at the interfaces between the p-typeregion 524 and the insulator layer 515 and the n-type region 526 and theinsulator layer 515. The carrier accumulation will result in thegeneration of an electric field in the optically active region as wellas potentially in the cladding regions surrounding the optically activeregion. The use of the high-κ material for the cladding material 550will, for a given change index of refraction, enable the use of lowerbias voltages and consume less energy than conventional designs in whichthe cladding regions surrounding the waveguide core do not incorporatehigh-κ materials.

FIG. 6 is a simplified schematic diagram illustrating adielectric-waveguide-dielectric structure incorporating high-κ materialsaccording to an embodiment of the present invention. Thedielectric-waveguide-dielectric structure illustrated in FIG. 6 sharessimilarities with the p-n diode waveguide structure illustrated in FIG.3 and the discussion provided in relation to FIG. 3 is applicable toFIG. 6 as appropriate.

Referring to FIG. 6, the cross-section of thedielectric-waveguide-dielectric structure includes an illustration ofsubstrate 610, which supports waveguide layer 620, which includeswaveguide core 640. In some embodiments, the substrate 610 is the buriedoxide (BOX) layer of a silicon-on-insulator (SOI) structure, althoughthis is not required by the present invention. Metal contacts 630 and632 are provided to enable application of a voltage bias across thesilicon waveguide core 640. Cladding material 650 disposed on eitherside of the silicon waveguide core 640 is fabricated using a high-κmaterial, for example, hafnium oxide (HfO₂).

In order to vary the index of refraction in the waveguide core 640, avoltage bias is applied using metal contacts 630 and 632, also referredto as electrodes. Since there is no current conduction path in thedielectric-waveguide-dielectric structure, the bias applied to theelectrodes will be dropped across the dielectric region 652 betweenmetal contact 630 and the waveguide core 640, the waveguide core 640,and the dielectric region 654 between the waveguide core 640 and metalcontact 632. In addition to use of high-κ materials for the claddingmaterial, dielectric region 652 and/or dielectric region 654 can alsoutilize high-κ materials. Moreover, substrate 610 can utilize high-κmaterial in some embodiments.

As discussed above, the incorporation of the high-κ cladding materialwill result in an increased percentage of the electric field beingdropped across the waveguide core, thereby either increasing the indexof refraction change at a given voltage bias or providing a given indexof refraction change at a lower voltage bias.

It should be noted that a “vertical” implementation of thedielectric-waveguide-dielectric structure incorporating high-κ materialsillustrated in FIG. 6 are included within the scope of the presentinvention. Dielectric region 652 and 654, as well as waveguide core 640can be formed using epitaxial processes to form a verticalimplementation that will share common elements with the embodimentillustrated in FIG. 6 and provide benefits of smaller device geometry aswell as other benefits. One of ordinary skill in the art would recognizemany variations, modifications, and alternatives.

According to some embodiments, the active photonic devices describedherein utilize electro-optic effects, such as free carrier inducedrefractive index variation in semiconductors, the Pockels effect, and/orthe DC Kerr effect to implement modulation and/or switching of opticalsignals. In conventional active photonic devices, although electro-opticmaterials can be utilized to form the waveguide core, materialscharacterized by small electro-optic coefficients, particularlymaterials having a small DC Kerr effect coefficient (i.e., the Kerrcoefficient χ⁽³⁾) are utilized to form the waveguide cladding. In theseconventional devices, the overlap between the applied electric field andthe optical mode(s) is present in both the waveguide core and thewaveguide cladding regions, resulting in inefficient modulation becausethe waveguide cladding utilizes materials with small electro-opticvalues, thereby resulting in minimal variation in the index ofrefraction as a function of the applied electric field in the waveguidecladding.

As described herein, some embodiments of the present invention provideactive photonic devices that use electro-optic materials for both thewaveguide core and the waveguide cladding. In terms of the waveguidestructure, the active photonic devices utilize a first type ofelectro-optic material characterized by a first (e.g., high) index ofrefraction as the waveguide core and a second type of electro-opticmaterial with a second (e.g., low) index of refraction as the waveguidecladding. Accordingly, the index changes for the waveguide structureresult from contributions provided by both the core and claddingmaterials, thereby enhancing the optical modulation produced at a givenapplied electric field.

Although some embodiments of the present invention are discussed inrelation to materials characterized by a large DC Kerr effect (whichresults from a large third order non-linear susceptibility, χ⁽³⁾), otherembodiments utilize materials characterized by a high Pockelscoefficient (which results from a large second order non-linearsusceptibility, χ⁽²⁾). Thus, both of these electro-optical coefficientsare included within the scope of the present invention. As describedherein, in some embodiments, the DC Kerr effect is the dominant effectin achieving index of refraction change since, as described below,unstrained silicon has a Pockels coefficient equal to zero. Thus, the DCKerr effect produced in the silicon waveguide portions of the structurecan be enhanced by the Pockels effect produced in the cladding portionsof the structure. In some conventional silicon photonics devices, thePockels effect is utilized. In these devices, materials that have a highelectro-optic effect have been utilized as internal layers in slotwaveguide structures, but the use of cladding materials with a highelectro-optic effect is generally discouraged because their typicallylow index of refraction compared to silicon results in a low waveguideconfinement factor.

FIG. 7A is a simplified schematic diagram illustrating a p-n diodewaveguide structure incorporating electro-optic cladding materialsaccording to an embodiment of the present invention. Referring to FIG.7A, the cross-section of the p-n diode waveguide structure includes anillustration of substrate 710, which supports waveguide layer 720, whichincludes p+ contact region 722, p-type region 724, n-type region 726,and n+ contact region 728. In some embodiments, the substrate 710 is theburied oxide (BOX) layer of a silicon-on-insulator (SOI) structure,although this is not required by the present invention. Metal contacts730 and 732 are provided to enable application of a voltage bias acrossthe silicon waveguide core 740.

The cladding for the waveguide structure includes a first claddingmaterial 745 that is disposed above and on either side of the siliconwaveguide core 740 and a second cladding material 746 that is disposedabove and on either side of the first cladding material 745. The firstcladding material is characterized by an electro-optic coefficient, forexample, a Kerr coefficient χ⁽³⁾ that is greater than the Kerrcoefficient associated with the waveguide core 740 or a Pockelscoefficient χ⁽²⁾ that is greater than the Pockels coefficient associatedwith the waveguide core 740. As an example, silicon can be utilized asthe waveguide core material 740, tantalum oxide (Ta₂O₅) can be utilizedas the first waveguide cladding material 745, and silicon dioxide (SiO₂)can be used as the second cladding material 746. Other suitablematerials for the first waveguide cladding material and/or the secondwaveguide cladding material include lead zirconate titanate(Pb[Zr_((x))Ti_((1-x))]O₃) (PZT), barium titanate (BaTiO₃), strontiumbarium niobate ((Sr,Ba)Nb₂O₆), combinations thereof, and the like.

Although different materials are illustrated for the first claddingmaterial 745 and the second cladding material 746, this is not requiredby the present invention and the same material can be utilized for boththe first and second cladding layers. As an example, the entire claddingcould be fabricated using tantalum oxide (Ta₂O₅), in which case, therewould be no distinction between the first cladding material and thesecond cladding material. In other embodiments, different compositionsof the same material could be utilized as the first cladding materialand the second cladding material. Moreover, although only two claddinglayers are illustrated in FIG. 7A, it will be appreciated that more thantwo cladding layers could be used, for example, a thin film of a firstcladding material (e.g., tantalum oxide (Ta₂O₅)), a thin film of asecond cladding material (e.g., HfO₂) deposited after the first claddingmaterial, N additional thin films of subsequent cladding materials, anda blanket coating of a final cladding material. Moreover, although asingle layer of the first cladding material is illustrated in FIG. 7A,this single “layer” can be made up of multiple sub-layers of differentmaterials or the same material. One of ordinary skill in the art wouldrecognize many variations, modifications, and alternatives.

Thus, in contrast with conventional designs in which the electro-opticalcoefficient associated with the waveguide cladding is less than theelectro-optical coefficient associated with the waveguide core,embodiments of the present invention utilize a waveguide design in whichthe electro-optical coefficient associated with the waveguide claddingis greater than the electro-optical coefficient associated with thewaveguide core. Moreover, some embodiments of the present inventionutilize low-loss waveguide structures that can be produced usingstandard silicon photonics foundry processes. Thus, slot waveguidestructures characterized by high loss are not compatible with thedesigns provided by some embodiments of the present invention.

Since silicon has a crystal structure that is centrosymmetric, siliconhas a Pockels coefficient that is equal to zero. Accordingly, someembodiments of the present invention utilize a waveguide cladding with aχ⁽²⁾ value greater than zero. If the silicon waveguide is fabricatedusing strained silicon, the waveguide cladding can have a χ⁽²⁾ valuegreater than the χ⁽²⁾ value for the strained silicon. In otherembodiments, the waveguide cladding can exhibit a significant DC Kerreffect (i.e., via a χ⁽³⁾ value that is greater than the χ⁽³⁾ value forsilicon).

Because, in the waveguide structure illustrated in FIG. 7A, the opticalmode propagating in the waveguide structure and the applied electricfield overlaps with both the waveguide core and waveguide cladding, thehigh electro-optical coefficient characterizing the first cladding willresult in a significant index of refraction variation in the firstcladding in addition to that produced in the waveguide core as a resultof the application of the electric field across the waveguide structure.Thus, embodiments of the present invention contrast with conventionaldesigns in which cladding material with a smaller electro-opticalcoefficient than the core is utilized, resulting in little variation ofthe index of refraction in the cladding material. Accordingly, inembodiments in which current injection is utilized to produce an indexchange in the waveguide core, as well as in embodiments in which anapplied electric field is utilized to produce an index change in thewaveguide core, the presence of the cladding characterized by a highelectro-optical coefficient can result in an increase in the indexchange produced for a given applied voltage.

As will be evident to one of skill in the art, current can be used toinduce a change in the real and imaginary index via free carrierelectrorefraction or electroabsorption, respectively (i.e., by changingthe carrier concentration in the optically active region). Thus,embodiments of the present invention can utilize either current-basedprocesses or DC Kerr and Pockels effects, which can be utilized in thecladding as a result of the applied electric field. In devices thatutilize both effects, current-based effects can operate in conjunctionwith index variation resulting from an applied electric field.

According to embodiments of the present invention, the thickness of thefirst cladding material 745 is sufficient to enable sufficient overlapbetween the optical mode and the first cladding material to achieve adesired variation in the index of refraction associated with the firstcladding layer. As an example, the thickness of the first cladding layer745 can range from about 10 nm to about 1 μm, for example, between tensof nanometers and hundreds of nanometers. As a result, the electricfield lines extending from the p-type region 724 to the n-type region726 will pass, not only through the waveguide core 740, but through thefirst cladding material disposed on either side of the waveguide core,as well as through at least a portion of the first cladding materialdisposed above the waveguide core. As described herein, theincorporation of cladding material with an electro-optical coefficientgreater than that associated with the waveguide core enables increasedvariation in the index of refraction of the waveguide structure for agiven voltage bias and applied electric field or a given variation inthe index of refraction of the waveguide structure for a reduced voltagebias and applied electric field. Additionally, incorporation of claddingmaterial with an electro-optical coefficient greater than thatassociated with conventional cladding materials can also be utilized.

As will be evident to one of skill in the art, the applied electricfield distribution is inversely proportional to the dielectric constant.As a result, in waveguide structures, for which the dielectric constantof the core is higher than or similar to the dielectric constant of thecladding, the applied electric field in the cladding region issignificant. Therefore, embodiments of the present invention utilizethis fact to provide for effective use of the applied electric field inthe cladding region by incorporating electro-optic materials in thecladding region.

In addition to cladding materials characterized by a Kerr coefficientχ⁽³⁾ that is greater than the Kerr coefficient associated with thewaveguide core (or a conventional cladding), combinations of both linear(i.e., Pockels effect) and non-linear (i.e., Kerr effect) electro-opticmaterials can be utilized. Thus, in an embodiment, silicon relying onthe Kerr effect can be utilized as the waveguide core material and PZTrelying on the Pockels effect can be utilized as the first claddingmaterial or the second cladding material. As another example, discussedabove, silicon relying on the Kerr effect can be utilized as thewaveguide core material and tantalum oxide (Ta₂O₅) also relying on theKerr effect can be utilized as the first cladding material or the secondcladding material. Thus, some embodiments utilize a structure in whichthe Kerr coefficient for the cladding is greater than the Kerrcoefficient for the core. In other embodiments, the Pockels coefficientsquared for the cladding is greater than the Kerr coefficient for thecore. Combinations of materials and material properties are thusincluded within the scope of the present invention.

Since a variety of materials are suitable for use with embodiments ofthe present invention, with a significant degree of freedom for materialchoice and combination, CMOS compatible materials can be utilized. Aswill be evident to one of skill in the art, CMOS compatible materialsprovide the advantages of scalability and integration for large scalecircuits using CMOS processes. Merely by way of example, Table 1 listsrepresentative optical properties for several CMOS compatible materialsthat can be utilized for either the first cladding material or thesecond cladding material.

TABLE 1 Refractive Index Dielectric Material χ⁽³⁾ (m²/W) (at 1.55 μm)Constant Si 2.2 × 10⁻¹⁸ ~3.5 11.7 Si₃N₄   2 × 10⁻¹⁹ 2 7-8 1.6 × 10⁻¹⁸2.5   2 × 10⁻¹⁸ 2.7 Ta₂O₅ 1 × 10⁻¹⁸-4 × 10⁻¹⁸ 2.08 25-50 TiO₂ 5 ×10⁻¹⁸-6 × 10⁻¹⁷ 2.27-2.6 10-85 Graphene 4.5 × 10⁻¹⁴ 2.2 ( at 1.2 μm) 2-50 Oxide

FIG. 7E is a simplified schematic diagram illustrating a waveguidestructure incorporating electro-optic cladding materials according to anembodiment of the present invention. The embodiment illustrated in FIG.7E is similar to that illustrated in FIG. 7A, but does not utilize a p-njunction in waveguide core 740. Rather, an undoped region 751 (e.g.,undoped silicon) is utilized in waveguide core 740, which is a pinjunction. Otherwise, the description provided in relation to FIG. 7A isapplicable to the embodiment illustrated in FIG. 7E as appropriate. Oneof ordinary skill in the art would recognize many variations,modifications, and alternatives.

FIG. 7B is a simplified schematic diagram illustrating a p-n diodewaveguide structure incorporating a planar electro-optic cladding layeraccording to an embodiment of the present invention. The structureillustrated in FIG. 7B shares common elements with the structuresillustrated in FIG. 7A and the discussion provided in relation to FIG.7A is applicable to the structure illustrated in FIG. 7B as appropriate.Referring to FIG. 7A, the cross-section of the p-n diode waveguidestructure includes an illustration of substrate 710, which supportswaveguide layer 750, which includes p+ contact region 752, p-type region754, n-type region 756, and n+ contact region 758. In some embodiments,the substrate 710 is the buried oxide (BOX) layer of asilicon-on-insulator (SOI) structure, although this is not required bythe present invention. Metal contacts 760 and 762 are provided to enableapplication of a voltage bias across the silicon waveguide core 764.

The waveguide core can be formed as a silicon ridge waveguide or othersuitable waveguide structure. After formation of the waveguide core 764,which can be a silicon waveguide core, a dielectric layer (e.g., SiO₂)is deposited and subsequently planarized to form a first portion of thewaveguide cladding. As illustrated in FIG. 7B, first dielectric region766 and second dielectric region 768 are disposed on either lateral sideof waveguide core 764. After planarization, a cladding layer 761 isformed as a second portion of the waveguide cladding using a material,in some embodiments, with an electro-optic coefficient greater than theelectro-optic coefficient characterizing the waveguide core. Thecladding layer 761 can be deposited using a deposition process or can betransferred using a layer transfer process.

The cladding layer 761 is characterized by an electro-optic coefficient,for example, a Kerr coefficient χ⁽³⁾ that is greater than the Kerrcoefficient associated with the waveguide core 764 or a Pockelscoefficient χ⁽²⁾ that is greater than the Pockels coefficient associatedwith the waveguide core 764. As an example, silicon can be utilized asthe waveguide core material 764, tantalum oxide (Ta₂O₅) can be utilizedas the cladding layer 761, and silicon dioxide (SiO₂) can be used as thematerial for the first portion of the waveguide cladding. As illustratedin FIG. 7B, one or more additional (optional) cladding layers 763 can beformed on the first cladding layer to provide the desired opticalconfinement. As an example, silicon dioxide (SiO₂) can be deposited onthe cladding layer 761 to form an additional cladding layer. Thecladding materials can utilize suitable materials as discussed inrelation to FIG. 7A.

Although different materials are illustrated in FIG. 7B for the firstportion of the waveguide cladding and the second portion of thewaveguide cladding, this is not required by the present invention andthe same material can be utilized for both the first portion of thewaveguide cladding and the second portion of the waveguide cladding. Asan example, after formation of the ridge waveguide, tantalum oxide(Ta₂O₅) could be deposited and planarized to form the first portion ofthe waveguide cladding and the second portion of the waveguide cladding.Alternatively, after formation of the ridge waveguide, tantalum oxide(Ta₂O₅) could be deposited and planarized to form the first portion ofthe waveguide cladding. Subsequently, a layer transfer process could beutilized to position cladding layer 761 above the waveguide core. Thediscussion of alternative materials and structures as described inrelation to FIG. 7A is applicable to the embodiment illustrated in FIG.7B as appropriate. One of ordinary skill in the art would recognize manyvariations, modifications, and alternatives.

In some embodiments, the width of the waveguide core is greater than theheight of the waveguide core. In these embodiments, interaction with thecladding material above and below the waveguide core will moresignificant than the interaction with the cladding material to the sidesof the waveguide core as a result of the differences in dimension.Therefore, in aligning the crystal axes of the cladding material to theapplied electric field, the dimensions of the structure as well as thegeometry and materials, which define the orientation of the appliedelectric field may be taken into consideration. As will be evident toone of skill in the art, the dielectric constant, the Pockels effect,and the Kerr effect are described by tensors and, therefore, embodimentsof the present invention can utilize specific geometries for crystallinematerials in which the crystallographic orientation relative to thedevice geometry provides desired properties for the cladding both on topof and next to the waveguide core.

Because embodiments of the present invention utilize the DC Kerr effectand/or the Pockels effect, the crystal orientation of the electro-opticmaterial is controlled to align the applied electric field with respectto the crystal axes of the electro-optic material in order to maximizethe electro-optic effect. Moreover, the polarization of the lightpropagating in the waveguide is aligned with respect to the crystal axesof the electro-optic material. Thus, alignment between the crystal axesand the applied electric field (e.g., at frequencies of gigahertz andbelow, which may be referred to as the “DC” electric field in contrastwith optical frequencies) as well as alignment between the crystal axesand the electric field of the optical mode (e.g., at opticalfrequencies) are implemented according to embodiments of the presentinvention. Moreover, the orientation of the waveguide (i.e. thepropagation direction of the light) with respect to the crystallographicaxes is also controlled in some embodiments.

For example, as illustrated in FIG. 7B, the electro-optic claddingmaterial 761 is characterized by crystal axes and electro-opticcoefficients characterized by a tensor. The crystal orientation of thecladding material, and the direction of propagation of the transmittedlight and its polarization direction, can be aligned so that the largestvalue of the electro-optic material coefficient tensor is utilized.Thus, in FIG. 7B, the crystal orientation of the cladding material issuch that the largest value of the electro-optic material coefficienttensor is utilized. As a result, the change in index of refractionproduced by the application of the applied electric field is maximized.As will be evident to one of skill in the art, the maximization of thesevalues is not required by the present invention and embodiments of thepresent invention include implementations in which coefficients of thePockels or Kerr effect tensors that are not the largest coefficients areutilized. These embodiments are included within the scope of the presentinvention.

Moreover, the polarization of the optical mode is selected to align theelectric field at optical frequencies with the largest value of theelectro-optic material coefficient tensor. Referring to FIG. 7B, if thepolarization of the optical mode is a transverse electric (TE) mode, theoptical electric field is polarized in the plane of the figure (e.g.,along the lateral direction) and perpendicular to the longitudinaldirection of the waveguide, which is normal to the plane of the figureand orthogonal to the lateral and transverse directions. Thus, theoptical electric field and the applied electric field are both alignedalong the lateral direction in an embodiment. In order to maximize theindex of refraction change produced by the applied electric field, thecrystal structure of the cladding material is aligned as discussedabove. As an example, barium titanate (BaTiO₃) is characterized by atetragonal crystal structure. Thus, for BaTiO₃, the c-axis is alignedalong the lateral direction with the a-axes perpendicular to the lateraldirection to achieve the largest electro-optic coefficient.

In some embodiments utilizing materials with non-cubic crystalstructures, the cladding material is formed such that half of thecrystallographic domains are oriented with their c-axis in a firstdirection in-plane direction and half of the domains are oriented in asecond direction in-plane direction perpendicular to the firstdirection. For these embodiments, the cladding material can be orientedsuch that the applied electric field and/or the optical electric fieldpolarization are perpendicular to the vector bisecting the firstdirection and the second direction, i.e., oriented at 45° to the firstdirection and the second direction to provide a component of the appliedelectric field that utilizes the largest of the electro-optic materialcoefficient tensor component. Thus, the index of refraction change dueto the applied electric field is maximized by optimizing the utilizationof the largest components of the Pockels and/or Kerr effect tensors. Oneof ordinary skill in the art would recognize many variations,modifications, and alternatives.

Thus, some embodiments of the present invention utilize the electrodegeometry (to define the orientation of the applied electric field), thecrystal orientation of the cladding material (to define theelectro-optic material tensor alignment), and/or the waveguide geometry(to define the optical electric field polarization and light propagationdirection) to ensure that the index of refraction change resulting fromthe DC Kerr effect (e.g., in both the silicon waveguide core and theelectro-optic material cladding) complements the index of refractionchange resulting from the Pockels effect in the electro-optic materialcladding. As described more fully in relation to FIGS. 12A-12D,embodiments utilize materials and structures that enable the DC Kerreffect to complement or work in conjunction with the Pockels effect,i.e., linear and non-linear electro-optic effects complementing eachother.

In FIGS. 12A-12D, the polarization domains in the thin film asillustrated by arrows pointing in either the positive z-direction or thenegative z-direction, which for the implementation shown in FIGS.12A-12D, is an in-plane direction. As illustrated at various appliedelectric fields, the polarization domains can be aligned with theapplied electric field as illustrated at 1210 and 1216 in FIG. 12B andat 1240 and 1246 in FIG. 12D or can be anti-aligned with the appliedelectric field as illustrated at 1212 and 1218 in FIG. 12B and at 1242and 1248 in FIG. 12D. Depending on the material type, i.e., a firstmaterial type as illustrated in FIGS. 12A and 12B or a second materialtype as illustrated in FIGS. 12C and 12D, the alignment of thepolarization domains with the applied electric field can result in anindex of refraction change that is either positive or negative. In FIGS.12A and 12B, the first material type results in a negative refractiveindex change due to an applied electric field when the polarizationdomains are aligned with the applied electric field. In FIGS. 12C and12D, the second material type results in a positive refractive indexchange due to an applied electric field when the polarization domainsare aligned with the applied electric field. In both cases, when thehalf of the polarization domains are aligned with the applied electricfield and half of the polarization domains are anti-aligned with theapplied electric field, the change in index of refraction due to anapplied electric field is approximately zero.

A one-dimensional model for the first material type is:

${\delta n} = {{\left( {\frac{n^{3}}{2}r_{eff}E_{z}} \right)\rho_{\downarrow z}} - {\left( {\frac{n^{3}}{2}r_{eff}E_{z}} \right)\rho_{\uparrow z}}}$where δn is the change in refractive index due to an applied fieldE_(z), r_(eff) is the effective Pockels coefficient, ρ_(↓z) is the areafraction of polarization domains that are polarized anti-parallel to thepositive z-direction, ρ_(↑z) is the area fraction of polarizationdomains that are polarized parallel to the positive z-direction. For thefirst material type, a negative index change occurs when the fraction ofpolarization domains that are polarized parallel to the applied electricfield E_(z) are greater than the fraction of polarization domains thatare polarized anti-parallel to the applied electric field E_(z).

A one-dimensional model for the second material type is:

${\delta n} = {{\left( {\frac{n^{3}}{2}r_{eff}E_{z}} \right)\rho_{\uparrow z}} - {\left( {\frac{n^{3}}{2}r_{eff}E_{z}} \right)\rho_{\downarrow z}}}$For the second material type, a positive index change occurs when thearea fraction of polarization domains that are polarized parallel to thepositive z-direction are greater than the area fraction of polarizationdomains that are polarized anti-parallel to the positive z-direction.

FIG. 12A is a graph plotting the DC Kerr effect as a function of appliedelectric field for a first material type according to an embodiment ofthe present invention. As illustrated in FIG. 12A, the DC Kerr effect ischaracterized by a positive index change for all applied voltages.

FIG. 12B is a graph plotting the refractive index change due to thePockels effect as a function of applied electric field for a firstmaterial type according to an embodiment of the present invention. Thepolarization direction of the polarization domains (i.e., aligned withthe positive z-direction or the negative z-direction) is hystereticdepending on the applied electric field because, as a result of theapplication of the electric field, the polarization direction can bemodified by the application of the electric field. Referring to 1210,the polarization direction of all polarization domains is aligned withthe positive z-direction. The applied electric field is also directed inthe positive z-direction. Since, for the first material type, a negativeindex change occurs when the fraction of polarization domains that arepolarized parallel to the applied electric field are greater than thefraction of polarization domains that are polarized anti-parallel to theapplied electric field, at 1210, the index change is negative.

As the amplitude of the applied electric field is reduced from thepositive value illustrated at 1210, the index change travels along curve1211, with the negative index change decreasing in absolute value towardzero at an applied electric field of zero. At 1212, a small negativeelectric field is oriented anti-parallel to the polarization domains,which are still mostly aligned with the positive z-direction, i.e.,ρ_(↑z)˜1, resulting in a positive index change. As the applied electricfield continues to decrease (i.e., a larger magnitude negative voltage),some of the polarization domains begin to flip to be polarized to alignwith the applied electric field and at 1214, ρ_(↑z)˜0.5 and ρ_(↓z)˜0.5,resulting in an index change of zero at applied electric field −E₁.Continued decrease in the applied electric field results in a decreasein the index change until all polarization domains are aligned with theapplied electric field at 1216.

As the amplitude of the applied electric field is decreased from thenegative value illustrated at 1216, the index change travels along curve1217, with the negative index change decreasing in absolute value towardzero at an applied electric field of zero. At 1218, a small positiveelectric field is oriented anti-parallel to the polarization domains,which are still mostly aligned with the negative z-direction, i.e.,ρ_(↓z)˜1, resulting in a positive index change. As the applied electricfield continues to increase, some of the polarization domains begin toflip to be polarized to align with the applied electric field and at1220, ρ_(↑z)˜0.5 and ρ_(↓)˜0.5, resulting in an index change of zero atapplied electric field E₂. Continued increases in the applied electricfield results in a decrease in the index change until all polarizationdomains are aligned with the applied electric field at 1210.

Referring to both FIGS. 12A and 12B, since the DC Kerr effect ispositive for all applied electric fields, operation between the voltages−E₁ and E₂ will result in positive index changes as a result of thePockels effect (i.e., −E₁<E_(z)<E₂).

FIG. 12C is a graph plotting the DC Kerr effect as a function of appliedelectric field for a second material type according to an embodiment ofthe present invention. As illustrated in FIG. 12C, the DC Kerr effect ischaracterized by a positive index change for all applied voltages.

FIG. 12D is a graph plotting the Pockels effect as a function of appliedelectric field for a second material type according to an embodiment ofthe present invention. In a manner similar to that discussed in relationto FIG. 12B, as the amplitude of the applied electric field is reducedfrom the positive value illustrated at 1240, the index change travelsalong curve 1241, with the positive index change decreasing in valuetoward zero at an applied electric field of zero. At 1242, a smallnegative electric field is oriented anti-parallel to the polarizationdomains, which are still mostly aligned with the positive z-direction,i.e., ρ_(↑z)˜1, resulting in a negative index change. As the appliedelectric field continues to decrease, some of the polarization domainsbegin to flip to be polarized to align with the applied electric fieldand at 1244, ρ_(↑z)˜0.5 and ρ_(↓z) ˜0.5, resulting in an index change ofzero at applied electric field −E₃. Continued decrease in the appliedelectric field results in a decrease in the index change until allpolarization domains are aligned with the applied electric field at1246.

As the amplitude of the applied electric field is decreased from thenegative value illustrated at 1246, the index change travels along curve1247, with the negative index change decreasing in absolute value towardzero at an applied electric field of zero. At 1248, a small positiveelectric field is oriented anti-parallel to the polarization domains,which are still mostly aligned with the negative z-direction, i.e.,ρ_(↓z)˜1, resulting in a negative index change. As the applied electricfield continues to increase, some of the polarization domains begin toflip to be polarized to align with the applied electric field and at1250, ρ_(↑z)˜0.5 and ρ_(↓z)˜0.5, resulting in an index change of zero atapplied electric field E₄. Continued increases in the applied electricfield results in a decrease in the index change until all polarizationdomains are aligned with the applied electric field at 1240.

Referring to both FIGS. 12C and 12D, since the DC Kerr effect ispositive for all applied electric fields, operation at voltages lessthan −E₃ and greater than E₄ will result in positive index changes as aresult of the Pockels effect (i.e., E_(z)<−E₁ or E₂<E_(z)). For thesecond type of material, regardless of the initial poling of thepolarization domains, operation at applied electric fields in the rangesE_(z)<−E₁ or E₂<E_(z) will result in a positive index change.Additionally, depending on the initial poling of the polarizationdomains, operation at lower voltages associated with positive indexchanges is possible along curve 1241, starting with positively poledmaterial (1240) and along curve 1247, starting with negative poledmaterial (1246). Some embodiments of the present invention utilizing thesecond type of material provide stability since operation at appliedelectric fields in the ranges E_(z)<−E₃ or E₄<E_(z) will result in theapplication of high fields to material that is polarized in the samedirection as the applied electric field. It should be noted that thelower operating biases illustrated in FIGS. 12A and 12B will result inlower power operation.

In some embodiments, the electro-optic material can be periodically ornon-periodically poled to established desired alignment of thepolarization domains. In other embodiments, operating at cryogenictemperatures, the polarization state may be maintained, obviating theneed for periodic poling operations.

FIG. 7C is a simplified schematic diagram illustrating a buriedwaveguide structure incorporating a planar electro-optic cladding layeraccording to an embodiment of the present invention. The structureillustrated in FIG. 7C shares common elements with the structuresillustrated in FIGS. 7A and 7B and the discussion provided in relationto FIGS. 7A and 7B is applicable to the structure illustrated in FIG. 7Cas appropriate. For purposes of clarity, the conductivity type of thevarious materials is not illustrated in FIG. 7C, but materials withdiffering conductivity as illustrated in FIGS. 7A and 7B can be utilizedin the structure illustrated in FIG. 7C as appropriate. As illustratedin FIG. 7C, substrate 710 supports buried waveguide 770, which isillustrated as positioned between first dielectric region 772, which asillustrated in FIG. 7C can be SiO₂, and second dielectric region 774,which as illustrated in FIG. 7C can be SiO₂. These first and seconddielectric regions 772 and 774 can be considered as a first portion ofthe waveguide cladding.

A cladding layer 775 is formed as a second portion of the waveguidecladding using a material with an electro-optic coefficient greater thanthe electro-optic coefficient characterizing the waveguide core. Thecladding layer 775 can be deposited using a deposition process or can betransferred using a layer transfer process. In some embodiments, thesecond portion of the waveguide cladding could use a material with anelectro-optic coefficient less than the electro-optic coefficientcharacterizing the waveguide core and still provide benefits notavailable using conventional cladding materials if the waveguidecladding has an electro-optic coefficient greater than that of aconventional cladding material.

The cladding layer 775 is characterized by an electro-optic coefficient,for example, a Kerr coefficient χ⁽³⁾ that is greater than the Kerrcoefficient associated with the waveguide core 770 or a Pockelscoefficient χ⁽²⁾ that is greater than the Pockels coefficient associatedwith the waveguide core 770. As an example, silicon can be utilized asthe waveguide core material 770, tantalum oxide (Ta₂O₅) can be utilizedas the cladding layer 775, and silicon dioxide (SiO₂) can be used as thematerial for the first dielectric region 772 and second dielectricregion 774 (i.e., the first portion of the waveguide cladding). Asillustrated in FIG. 7C, one or more additional cladding layers 777 canbe formed on the first cladding layer to provide the desired opticalconfinement. As an example, silicon dioxide (SiO₂) can be deposited onthe first cladding layer 775 to form an additional cladding layer 777.The cladding materials can utilize suitable materials as discussed inrelation to FIGS. 7A and 7B.

In order to establish an applied electric field extending through thecladding layer 775 and the waveguide core 770, a bias voltage is appliedto electrodes 730 and 732, which can be metal electrodes or othersuitable materials that provide electrical conductivity. In someembodiments, electrical contact is provided to the waveguide materials,which may include doped regions that form a p-n junction as illustratedin FIG. 7A, in order to prevent carrier screening that may result fromapplication of the electric field across the waveguide core.

FIG. 7D is a simplified schematic diagram illustrating a buriedwaveguide structure incorporating a planar electro-optic cladding layeraccording to another embodiment of the present invention. The structureillustrated in FIG. 7D shares common elements with the structuresillustrated in FIGS. 7A, 7B, and 7C and the discussion provided inrelation to FIGS. 7A, 7B, and 7C is applicable to the structureillustrated in FIG. 7D as appropriate. For purposes of clarity, theconductivity type of the various materials is not illustrated in FIG.7D, but materials with differing conductivity as illustrated in FIGS. 7Aand 7B can be utilized in the structure illustrated in FIG. 7D asappropriate. As illustrated in FIG. 7D, substrate 710 supports buriedwaveguide 780, which is illustrated as positioned above a planarcladding layer 782 and partially surrounded by a second cladding layer784.

Planar cladding layer 782 is formed using a material with anelectro-optic coefficient greater than the electro-optic coefficientcharacterizing the waveguide core 780. The planar cladding layer 782 canbe deposited using a deposition process or can be transferred using alayer transfer process. As discussed above, the planar cladding layercould use a material with an electro-optic coefficient less than theelectro-optic coefficient characterizing the waveguide core and stillprovide benefits not available using conventional cladding materials ifthe planar cladding has an electro-optic coefficient greater than thatof a conventional cladding material.

Planar cladding layer 782 is characterized by an electro-opticcoefficient, for example, a Kerr coefficient χ⁽³⁾ that is greater thanthe Kerr coefficient associated with the waveguide core 780 or a Pockelscoefficient χ⁽²⁾ that is greater than the Pockels coefficient associatedwith the waveguide core 780. As an example, silicon can be utilized asthe waveguide core material 780, tantalum oxide (Ta₂O₅) can be utilizedas planar cladding layer 782, and silicon dioxide (SiO₂) can be used asthe material for the second dielectric layer 784. The cladding materialscan utilize suitable materials as discussed in relation to FIGS. 7A, 7B,and 7C.

In order to establish an applied electric field extending through thecladding layer 782 and the waveguide core 780, a bias voltage is appliedto electrodes 730 and 732, which can be metal electrodes or othersuitable materials that provide electrical conductivity. In someembodiments, electrical contact is provided to the waveguide materials,which may include doped regions that form a p-n junction as illustratedin FIG. 7A, in order to prevent carrier screening that may result fromapplication of the electric field across the waveguide core.

FIG. 8 is a simplified schematic diagram illustrating a p-i-n diodewaveguide structure incorporating electro-optic cladding materialsaccording to an embodiment of the present invention. The p-i-n diodewaveguide structure illustrated in FIG. 8 shares similarities with thep-n diode waveguide structure illustrated in FIG. 4 and the discussionprovided in relation to FIG. 4 is applicable to FIG. 8 as appropriate.

Referring to FIG. 8, the cross-section of the p-i-n diode waveguidestructure includes an illustration of substrate 410, which supportswaveguide layer 420, which includes p+ contact region 422, p-type region424, intrinsic region 425, n-type region 426, and n+ contact region 428.In some embodiments, the substrate 410 is the buried oxide (BOX) layerof a silicon-on-insulator (SOI) structure, although this is not requiredby the present invention. Metal contacts 430 and 432 are provided toenable application of a voltage bias across the silicon waveguide core440.

The cladding for the waveguide structure includes a first claddingmaterial 745 that is disposed above and on either side of the siliconwaveguide core 740 and a second cladding material 746 that is disposedabove and on either side of the first cladding material 745. The firstcladding material can be referred to as a proximal cladding material 810since it is adjacent to and disposed on either side of the siliconwaveguide core 440 and the second cladding material can be referred toas a distal cladding material 450.

The first cladding material is characterized by an electro-opticcoefficient, for example, a Kerr coefficient χ⁽³⁾ that is greater thanthe Kerr coefficient associated with the waveguide core 440 or a Pockelscoefficient χ⁽²⁾ that is greater than the Pockels coefficient associatedwith the waveguide core 440. As an example, silicon can be utilized asthe waveguide core material 440, hafnium oxide (HfO₂) or tantalum oxide(Ta₂O₅) can be utilized as the first waveguide cladding material 810,and silicon dioxide (SiO₂) can be used as the second cladding material450. Other suitable materials for the first waveguide cladding materialand/or the second waveguide cladding material include lead zirconatetitanate (Pb[Zr_((x))Ti_((1-x))]O₃) (PZT), barium titanate (BaTiO₃),strontium barium niobate ((Sr,Ba)Nb₂O₆), combinations thereof, and thelike.

Although different materials are illustrated for the first claddingmaterial 810 and the second cladding material 450, this is not requiredby the present invention and the same material can be utilized for boththe first and second cladding layers. As an example, the entire claddingcould be fabricated using tantalum oxide (Ta₂O₅), in which case, therewould be no distinction between the first cladding material and thesecond cladding material. In other embodiments, different compositionsof the same material could be utilized as the first cladding materialand the second cladding material. Moreover, although only two claddinglayers are illustrated in FIG. 8, it will be appreciated that more thantwo cladding layers could be used, for example, a thin film of a firstcladding material (e.g., tantalum oxide (Ta₂O₅)), a thin film of asecond cladding material (e.g., HfO₂) deposited after the first claddingmaterial, N additional thin films of subsequent cladding materials, anda blanket coating of a final cladding material. Moreover, although asingle layer of the first cladding material is illustrated in FIG. 8,this single “layer” can be made up of multiple sub-layers of differentmaterials or the same material. One of ordinary skill in the art wouldrecognize many variations, modifications, and alternatives.

In order to vary the index of refraction in the waveguide core, avoltage bias is applied using metal contacts 430 and 432, also referredto as electrodes. As an example, the p-i-n junction can be placed underreverse bias, generating a depletion region in the intrinsic region 425.Thus, application of the reverse voltage bias will result in generationof an electric field in the waveguide core as well as in the claddingregions. As discussed above, the incorporation of the high-κ claddingmaterial will result in an increased percentage of the voltage biasbeing dropped across the waveguide core, thereby either increasing theindex of refraction change at a given voltage bias or providing a givenindex of refraction change at a lower voltage bias.

Although a silicon waveguide core and hafnium oxide first cladding canbe utilized in the embodiment illustrated in FIG. 8, other materials canbe utilized according to embodiments of the present invention. Forexample, in addition to silicon, other materials including SiN, Ge,SiGe, and various polymers can be utilized for the waveguide core.Moreover, in addition to hafnium dioxide, other materials includingtantalum oxide (Ta₂O₅), zirconium oxide (ZrO₂), titanium dioxide (TiO₂),other refractory metal oxides, combinations thereof, or the like can beutilized for the first waveguide cladding.

FIG. 9 is a simplified schematic diagram illustrating a vertical pinwaveguide structure incorporating high-κ materials according to anembodiment of the present invention. The vertical pin waveguidestructure illustrated in FIG. 9 shares similarities with the p-n diodewaveguide structure illustrated in FIG. 5 and the discussion provided inrelation to FIG. 5 is applicable to FIG. 9 as appropriate.

Referring to FIG. 9, the cross-section of the vertical pin waveguidestructure includes an illustration of substrate 510, which supportswaveguide region 520, which includes p+ contact region 522, p-typeregion 524, n-type region 526, and n+ contact region 528. The opticalwaveguide is defined by the p-type region 524, intrinsic silicon layer515, and the n-type region 526. In some embodiments, the substrate 510is the buried oxide (BOX) layer of a silicon-on-insulator (SOI)structure, although this is not required by the present invention. Metalcontacts 530 and 532 are provided to enable application of a voltagebias across the vertical pin formed by the p-type region 524, theintrinsic layer 515, and the n-type region 526.

The cladding for the waveguide structure includes a first claddingmaterial 910 that is disposed above, below, and on either side of thewaveguide structure and a second cladding material 550 that is disposedabove, below, and on either side of the first cladding material 910. Thefirst cladding material can be referred to as a proximal claddingmaterial since it is adjacent to and disposed on either side of thewaveguide structure and the second cladding material can be referred toas a distal cladding material.

The first cladding material 910 is characterized by an electro-opticcoefficient, for example, a Kerr coefficient χ⁽³⁾ that is greater thanthe Kerr coefficient associated with the waveguide structure or aPockels coefficient χ⁽²⁾ that is greater than the Pockels coefficientassociated with the waveguide structure. As discussed in relation toFIG. 8, hafnium oxide (HfO₂) or tantalum oxide (Ta₂O₅) can be utilizedas the first waveguide cladding material 910, and silicon dioxide (SiO₂)can be used as the second cladding material 550. Other suitablematerials for the first waveguide cladding material and/or the secondwaveguide cladding material include lead zirconate titanate(Pb[Zr_((x))Ti_((1-x))]O₃) (PZT), barium titanate (BaTiO₃), strontiumbarium niobate ((Sr,Ba)Nb₂O₆), combinations thereof, and the like.

Moreover, although different materials are illustrated for the firstcladding material 910 and the second cladding material 550, this is notrequired by the present invention and the same material can be utilizedfor both the first and second cladding layers. As an example, the entirecladding could be fabricated using tantalum oxide (Ta₂O₅), in whichcase, there would be no distinction between the first cladding materialand the second cladding material. In other embodiments, differentcompositions of the same material could be utilized as the firstcladding material and the second cladding material. Moreover, althoughonly two cladding layers are illustrated in FIG. 9, it will beappreciated that more than two cladding layers could be used, forexample, a thin film of a first cladding material (e.g., tantalum oxide(Ta₂O₅)), a thin film of a second cladding material (e.g., HfO₂)deposited after the first cladding material, N additional thin films ofsubsequent cladding materials, and a blanket coating of a final claddingmaterial. Moreover, although a single layer of the first claddingmaterial is illustrated in FIG. 9, this single “layer” can be made up ofmultiple sub-layers of different materials or the same material. One ofordinary skill in the art would recognize many variations,modifications, and alternatives.

In the vertical pin waveguide structure illustrated in FIG. 9, a guidedmode is supported with a peak amplitude that is generally aligned withthe intrinsic layer 515. The intrinsic layer 515 can be fabricated usinga suitable undoped or low-doped semiconductor, for example, silicon ifp-type region 524 and n-type region 526 are silicon. In someembodiments, the thickness of the intrinsic layer 515 ranges from about0 nm to about 100 nm, for example, 30 nm.

In some embodiments, biasing of the metal contacts 530 and 532 canresult in carrier accumulation at the interfaces between the p-typeregion 524 and the insulator layer 515 and the n-type region 526 and theinsulator layer 515. The carrier accumulation will result in thegeneration of an electric field in the optically active region as wellas potentially in the cladding regions surrounding the optically activeregion. The use of the large electro-optic coefficient material for thefirst cladding material 910 will, for a given change index ofrefraction, enable the use of lower bias voltages and consume lessenergy than conventional designs in which the cladding regionssurrounding the waveguide core do not incorporate large electro-opticcoefficient materials.

FIG. 10 is a simplified schematic diagram illustrating adielectric-waveguide-dielectric structure incorporating electro-opticcladding materials according to an embodiment of the present invention.The dielectric-waveguide-dielectric structure illustrated in FIG. 10shares similarities with the dielectric-waveguide-dielectric waveguidestructure illustrated in FIG. 6 and the discussion provided in relationto FIG. 6 is applicable to FIG. 10 as appropriate.

Referring to FIG. 10, the cross-section of thedielectric-waveguide-dielectric structure includes an illustration ofsubstrate 610, which supports waveguide layer 620, which includeswaveguide core 640. In some embodiments, the substrate 610 is the buriedoxide (BOX) layer of a silicon-on-insulator (SOI) structure, althoughthis is not required by the present invention. Metal contacts 630 and632 are provided to enable application of a voltage bias across thesilicon waveguide core 640.

The cladding surrounding the waveguide core 640 includes a firstcladding layer 1010 disposed below the waveguide core, lateral claddinglayers 1012 and 1014 disposed on either side of the waveguide core, andsecond cladding layer 1016 disposed above the waveguide core. Inaddition to first cladding layer 1010, lateral cladding layers 1012 and1014, and second cladding layer 1016, proximal dielectric regions 650,652, and 654 are disposed with one or more of the lateral claddinglayers 1012 and 1014 or second cladding layer 1016 between the proximaldielectric regions and the waveguide core.

First cladding layer 1010, lateral cladding layers 1012 and 1014, andsecond cladding layer 1016 are characterized by an electro-opticcoefficient, for example, a Kerr coefficient χ⁽³⁾ that is greater thanthe Kerr coefficient associated with waveguide core 640 or a Pockelscoefficient χ⁽²⁾ that is greater than the Pockels coefficient associatedwith waveguide core 640.

As an example, silicon can be utilized as the waveguide core 640 andhafnium oxide (HfO₂) or tantalum oxide (Ta₂O₅) can be utilized as firstcladding layer 1010, lateral cladding layers 1012 and 1014, and secondcladding layer 1016, and silicon dioxide (SiO₂) can be used as theproximal dielectric regions 650, 652, and 654. Other suitable materialsfor first cladding layer 1010, lateral cladding layers 1012 and 1014,and second cladding layer 1016 and/or proximal dielectric regions 650,652, and 654 include lead zirconate titanate (Pb[Zr_((x))Ti_((1-x))]O₃)(PZT), barium titanate (BaTiO₃), strontium barium niobate((Sr,Ba)Nb₂O₆), combinations thereof, and the like.

Although different materials are illustrated for first cladding layer1010, lateral cladding layers 1012 and 1014, and second cladding layer1016 and proximal dielectric regions 650, 652, and 654, this is notrequired by the present invention and the same material can be utilizedfor both first cladding layer 1010, lateral cladding layers 1012 and1014, and second cladding layer 1016 and proximal dielectric regions650, 652, and 654. As an example, the entire cladding could befabricated using tantalum oxide (Ta₂O₅), in which case, there would beno distinction between first cladding layer 1010, lateral claddinglayers 1012 and 1014, and second cladding layer 1016 and proximaldielectric regions 650, 652, and 654. In other embodiments, differentcompositions of the same material could be utilized as the variouscladding materials. Moreover, although only two cladding layers areillustrated in FIG. 10, it will be appreciated that more than twocladding layers could be used, for example, a thin film of a firstcladding material (e.g., tantalum oxide (Ta₂O₅)), a thin film of asecond cladding material (e.g., HfO₂) deposited after the first claddingmaterial, N additional thin films of subsequent cladding materials, anda blanket coating of a final cladding material. Moreover, although asingle layer of cladding material is illustrated in FIG. 10 for firstcladding layer 1010, lateral cladding layers 1012 and 1014, and secondcladding layer 1016, these single “layers” can be made up of multiplesub-layers of different materials or the same material. One of ordinaryskill in the art would recognize many variations, modifications, andalternatives.

In order to vary the index of refraction in waveguide core 640, avoltage bias is applied using metal contacts 630 and 632, also referredto as electrodes. Since there is no current conduction path in thedielectric-waveguide-dielectric structure, the bias applied to theelectrodes will be dropped across the dielectric region 652 betweenmetal contact 630 and the waveguide core 640, the waveguide core 640,and the dielectric region 654 between the waveguide core 640 and metalcontact 632. In addition to use of large electro-optic coefficientmaterials for the first cladding layer 1010, lateral cladding layers1012 and 1014, and second cladding layer 1016, dielectric region 652and/or dielectric region 654 can also utilize large electro-opticcoefficient materials. Moreover, substrate 610 can utilize largeelectro-optic coefficient materials in some embodiments.

As discussed above, the incorporation of the large electro-opticcoefficient materials for one or more cladding layers will result in anincreased percentage of the electric field being dropped across thewaveguide core, thereby either increasing the index of refraction changeat a given voltage bias or providing a given index of refraction changeat a lower voltage bias.

It should be noted that a “vertical” implementation of thedielectric-waveguide-dielectric structure incorporating largeelectro-optic coefficient materials illustrated in FIG. 10 are includedwithin the scope of the present invention. Dielectric region 652 and654, as well as waveguide core 640 can be formed using epitaxialprocesses to form a vertical implementation that will share commonelements with the embodiment illustrated in FIG. 10 and provide benefitsof smaller device geometry as well as other benefits. One of ordinaryskill in the art would recognize many variations, modifications, andalternatives.

FIG. 11 is a simplified system diagram illustrating incorporation of anelectro-optic switch with a cryostat according to an embodiment of thepresent invention. In order to operate at low temperatures, for exampleliquid helium temperatures, embodiments of the present inventionintegrate the electro-optic switches discussed herein into a system thatincludes cooling systems. Thus, embodiments of the present inventionprovide a hybrid computing system, for example, as illustrated in FIG.11. The hybrid computing system 1101 includes a user interface device1103 that is communicatively coupled to a hybrid quantum computing (QC)sub-system 1105. The user interface device 1103 can be any type of userinterface device, e.g., a terminal including a display, keyboard, mouse,touchscreen and the like. In addition, the user interface device canitself be a computer such as a personal computer (PC), laptop, tabletcomputer and the like. In some embodiments, the user interface device1103 provides an interface with which a user can interact with thehybrid QC subsystem 1105. For example, the user interface device 1103may run software, such as a text editor, an interactive developmentenvironment (IDE), command prompt, graphical user interface, and thelike so that the user can program, or otherwise interact with, the QCsubsystem to run one or more quantum algorithms. In other embodiments,the QC subsystem 1105 may be pre-programmed and the user interfacedevice 1103 may simply be an interface where a user can initiate aquantum computation, monitor the progress, and receive results from thehybrid QC subsystem 1105. Hybrid QC subsystem 1105 further includes aclassical computing system 1107 coupled to one or more quantum computingchips 1109. In some examples, the classical computing system 1107 andthe quantum computing chip 1109 can be coupled to other electroniccomponents 1111, e.g., pulsed pump lasers, microwave oscillators, powersupplies, networking hardware, etc.

In some embodiments that utilize cryogenic operation, the quantumcomputing system 1109 can be housed within a cryostat, e.g., cryostat1113. In some embodiments, the quantum computing chip 1109 can includeone or more constituent chips, e.g., hybrid electronic chip 1115 andintegrated photonics chip 1117. Signals can be routed on- and off-chipany number of ways, e.g., via optical interconnects 1119 and via otherelectronic interconnects 1121. In addition, the hybrid computing system1101 may employ a quantum computing process, e.g., measurement-basedquantum computing (MBQC) that employs one or more cluster states ofqubits.

It is also understood that the examples and embodiments described hereinare for illustrative purposes only and that various modifications orchanges in light thereof will be suggested to persons skilled in the artand are to be included within the spirit and purview of this applicationand scope of the appended claims.

What is claimed is:
 1. An optical device comprising: a substrate; afirst electrical contact; a second electrical contact; and a waveguidestructure disposed between the first electrical contact and the secondelectrical contact and comprising: a waveguide core coupled to thesubstrate and including a first material characterized by a first indexof refraction and a first electro-optic coefficient; and a waveguidecladding at least partially surrounding the waveguide core and includinga second material characterized by a second index of refraction lessthan the first index of refraction and a second electro-opticcoefficient greater than the first electro-optic coefficient.
 2. Theoptical device of claim 1 wherein the first electro-optic coefficientand the second electro-optic coefficient are the Kerr coefficient χ⁽³⁾.3. The optical device of claim 1 wherein the first electro-opticcoefficient and the second electro-optic coefficient are the Pockelscoefficient χ⁽²⁾.
 4. The optical device of claim 1 wherein the waveguidecore supports a guided mode characterized by an optical power, wherein amajority of the optical power is contained in the waveguide core.
 5. Theoptical device of claim 1 wherein the waveguide core comprises silicon.6. The optical device of claim 5 wherein the waveguide core comprisessilicon nitride.
 7. The optical device of claim 1 wherein the firstelectro-optic coefficient equals approximately zero.
 8. The opticaldevice of claim 1 wherein the waveguide core supports a TE polarizationmode.
 9. The optical device of claim 1 wherein: the first electricalcontact and the second electrical contact are configured to generate anapplied electric field produced in the waveguide structure that ischaracterized by a direction; and the waveguide cladding ischaracterized by an electro-optic coefficient tensor having a maximumvalue aligned along the direction.
 10. The optical device of claim 9wherein a guided mode supported by the waveguide core has a direction ofpolarization aligned with the direction.
 11. The optical device of claim9 wherein the waveguide cladding is characterized by a DC Kerr effectand a Pockels effect having a same sign.
 12. The optical device of claim11 wherein the DC Kerr effect is positive and the Pockels effect ispositive.
 13. The optical device of claim 12 wherein the waveguidecladding comprises a first material type, a majority of polarizationdomains are aligned with a positive z-direction, and a direction of theapplied electric field is negative.
 14. The optical device of claim 12wherein the waveguide cladding comprises a first material type, amajority of polarization domains are aligned with a negativez-direction, and a direction of the applied electric field is positive.15. The optical device of claim 12 wherein the waveguide claddingcomprises a second material type, a majority of polarization domains arealigned with a positive z-direction, and a direction of the appliedelectric field is positive.
 16. The optical device of claim 12 whereinthe waveguide cladding comprises a second material type, a majority ofpolarization domains are aligned with a negative z-direction, and adirection of the applied electric field is negative.